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MULTI-RESOLUTION REPRESENTATION OF DIGITAL TERRAIN MODELS 
WITH TOPOGRAPHICAL FEATURES PRESERVATION 
Zhi Wang a,b ’ *, Qingquan Li a , Besheng Yang® 
a State Key Laboratory for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, 
Luoyu Road, Wuhan, China, 430079 - wangzchina@gmail.com, (qqli, bshyang)@whu.edu.cn 
b Institut fur Kartographie und Geoinformatik, Leibniz Universität, Hannover, Appelstraße 9a, 
D-30167 Hannover, Germany 
Youth Forum 
KEY WORDS: Geometry, Geomorphology, Extraction, Simplification, Feature, Multi-resolution 
ABSTRACT: 
Multi-resolution TIN model is a promising solution for achieving rapid visualization speed and interactive frame rates in the 
contexts of visualization, virtual reality (VR), and geographic information systems (GIS). Most of previous automatic algorithms are 
not able to identify topographic features, such as peak, pit, ridge, channel and pass, so as to produce poor approximations when a 
model is simplified to a low level of detail. This paper proposes a new method for constructing multi-resolution TIN models with 
multi-scale topographic feature preservation. The proposed method is driven by a half-edge collapse operation in a greedy 
framework and employs a new quadric error metric to efficiently measure geometric errors. We define topographic features in a 
multi-scale manner using a center-surround operator on Gaussian-weighted mean curvatures. Then we employ an adaptive weight 
based on topographic features for the control of simplification process. Experimental results identify that proposed method performs 
better than previous methods in terms of topographic feature preservation, and can achieve multi-resolution TIN models with a 
higher accuracy. 
1. INTRODUCTION 
High-resolution terrain model leads to a dilemma between the 
rendering time, interactive frame rates, and data processing. A 
model with a fixed resolution is not good for all applications 
and all users because of different requirements, available 
computer resources, and affordable time. Therefore, it would be 
ideal for users to have the ability to control the size of the 
model, the processing time needed, and the accuracy of the 
model. The representation of digital terrain models at different 
levels of accuracy and resolution has an impact on applications 
such as Geographic Information Systems (GISs), Virtual 
Reality (VR), progressive transmission of spatial data, mobile 
visualizations, and Web-GIS. Multi-resolution terrain models 
allow for representation, analysis and manipulation of terrain 
data at variable resolutions, decreasing the burden of rendering 
and achieving interactive frame rates, and provide a promising 
solution for the progressive transmission of spatial data, spatial 
data compression, mobile visualizations, and so on. However, 
the existing methods and algorithms mainly focus on the 
accuracy and running times of generating the levels-of-details 
(LoDs) of terrains. Less attention has been paid to topographic 
features preservation of terrains, particularly at a low resolution 
model. Suppose that the original topographic features are lost at 
a low resolution terrain model. Poor visualization effects and 
spatial analysis results will be generated. 
In this paper, we propose an algorithm for generating multi 
resolution terrain models with a good performance in terms of 
good preservation of topographic features and rapid running 
time. Two key issues are encompassed in the proposed method, 
namely, measuring deviations between the original terrain 
model and its approximations based on a new error metric, 
detecting and adaptively ranking topographic features based on 
the Gaussian-weighted of surface curvatures. The former one 
aims to achieve rapid running time; the latter one aims to 
preserve topographic features during the generation of multi 
resolution TIN models hence improve the accuracy of multi 
resolution models in terms of the RMSEs and Hausdorff 
distances (Hausdorff distance is defined as the maximal 
Euclidean distance between any point of original model and the 
closest point of its approximation.). 
2. PREVIOUS WORK 
There has been extensive research work on generating multi 
resolution models. In this section, we review previous work, 
focusing on only those contributions most relevant to this paper. 
Readers can refer to Luebke D. et al. (2003) for the surveying 
of these simplification schemes. The local operators including 
vertex removal, edge collapse, and triangle collapse, are 
commonly used for generating multi-resolution models. Among 
these local operators, edge collapse and triangle collapse 
operators can be conceptualized as gradually shrinking the 
appropriate geometric primitive such as edge and triangle to a 
single vertex. Therefore, they are well suited for implementing 
geomorphing between successive LoDs. Moreover, the 
advantage of the iterative edge collapse operator is its 
hierarchical structure which is essential to retaining the 
topological relationship of the model. The main difference 
among these edge collapse algorithms is in the selection of the 
candidate edges and determination of new vertices. Garland and 
Heckbert (1997) proposed quadric error metrics (QEM) and, 
Corresponding author: Zhi Wang: wangzchina@gmail.com